There are only two times this phrase is used:
γεγέννημαι ►
Englishman's Concordance
γεγέννημαι (gegennēmai) — 2 Occurrences
John 18:37 V-RIM/P-1S
GRK: εἰς τοῦτο γεγέννημαι καὶ εἰς
NAS: For this I have been born, and for this
KJV: end was I born, and for
INT: for this I have been born and for
Acts 22:28 V-RIM/P-1S
GRK: δὲ καὶ γεγέννημαι
NAS: But I was actually born [a citizen].
KJV: But I was [free] born.
INT: however also was [free] bor
We can see what
Paul means when that phrase was born is used as an example of what he was born with. It was because of his family line and where he was born that made him a Roman citizen when he came out of the womb.
Paul was born as a citizen of Rome and freedom that it represented.
In the same way when Jesus came out of the womb he was born as King from His Father's lineage as the Word of God became flesh.
The verse In Micah also bears witness who is coming forth in labor.
And you, Beth-Lehem Ephratah, Little to be among the chiefs of Judah! From you He comes forth to Me—to be ruler in Israel, And His comings forth [are] of old, From the days of antiquity.” Micah 5:2
3Therefore, He will give them up until the time
When she who is in labor has given birth to a child.
One can see the three times this same word is used as a woman in labor.
◄ yō·w·lê·ḏāh ►
Englishman's Concordance
yō·w·lê·ḏāh — 3 Occurrences
Isaiah 21:3
HEB: אֲחָז֔וּנִי כְּצִירֵ֖י יֽוֹלֵדָ֑ה נַעֲוֵ֣יתִי מִשְּׁמֹ֔עַ
NAS: me like the pains of a woman in labor. I am so
KJV: upon me, as the pangs of a woman that travaileth: I was bowed down
INT: have seized the pains labor bewildered hear
Hosea 13:13
HEB: חֶבְלֵ֥י יֽוֹלֵדָ֖ה יָבֹ֣אוּ ל֑וֹ
NAS: The pains of childbirth come
KJV: The sorrows of a travailing woman shall come
INT: the pains of childbirth come he
Micah 5:3
HEB: עַד־ עֵ֥ת יוֹלֵדָ֖ה יָלָ֑דָה וְיֶ֣תֶר
NAS: the time When she who is in labor has borne
KJV: until the time [that] she which travaileth hath brought forth:
INT: them until the time labor has borne the remainde
The three wisemen also bear witness of a King that was born out of a womb.
"Where is he who is born King of the Jews? For we saw his star in the east, and have come to worship him."Matthew 2:2
We also see that this King of Israel is also the son of God.
Nathanael answered and saith to him, 'Rabbi, thou art the Son of God, thou art the king of Israel.' John 1:49
Later on we see this King that was born out of a womb is now dying on the cross
Over His head they placed a written statement of the charge against Him: THIS IS JESUS THE KING OF THE JEWS. Matthew 27:37
OP's question,
What contextual or grammatical clues do we have to tell us whether the 'born' at John 18:37 is referring to Jesus' literal (biological) birth, a spiritual birth, or perhaps both?
Definitely would say it's a mixture of both spirit and flesh being born and brought forth as a son of Adam and God.